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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Spectral Equivalence Properties of Higher-Order Tensor Product Finite Elements and Applications to Preconditioning

In this study, we present spectral equivalence results for higher-order tensor product edge-, face- and interior-based finite elements. Specifically, we show for certain choices of shape functions that the mass and stiffness matrices of the higher-order elements are spectrally equivalent to those for an assembly of lowest-order elements on the associated Gauss-Lobatto-Legendre mesh. Based on this equivalence, efficient preconditioners can be designed with favorable computational complexity. Numerical results are presented which confirm the theory and demonstrate the benefits of the equivalence results for overlapping Schwarz preconditioners.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Signal Preconditioning to Minimize Impulse Response Contribution

A study was performed to identify a method to minimize the effect of a linear time-invariant (LTI) system impulse response on an input. Three methods were studied: Wiener filter, the N4SID algorithm and transfer function estimation, the latter two using functions from MATLAB’s System Identification Toolbox. Although all three methods were able estimate an unknown forward impulse response given an input/output time series pair, only the Wiener filter was able to estimate a system inverse which satisfactorily solved the problem using a cosine similarity measure.

42 ENGINEERING↗
DOE OSTI2022

Randomized Cholesky Preconditioning for Graph Partitioning Applications

A graph is a mathematical representation of a network; we say it consists of a set of vertices, which are connected by edges. Graphs have numerous applications in various fields, as they can model all sorts of connections, processes, or relations. For example, graphs can model intricate transit systems or the human nervous system. However, graphs that are large or complicated become difficult to analyze. This is why there is an increased interest in the area of graph partitioning, reducing the size of the graph into multiple partitions. For example, partitions of a graph representing a social network might help identify clusters of friends or colleagues. Graph partitioning is also a widely used approach to load balancing in parallel computing. The partitioning of a graph is extremely useful to decompose the graph into smaller parts and allow for easier analysis. There are different ways to solve graph partitioning problems. For this work, we focus on a spectral partitioning method which forms a partition based upon the eigenvectors of the graph Laplacian (details presented in Acer, et. al.). This method uses the LOBPCG algorithm to compute these eigenvectors. LOBPCG can be accelerated by an operator called a preconditioner. For this internship, we evaluate a randomized Cholesky (rchol) preconditioner for its effectiveness on graph partitioning problems with LOBPCG. We compare it with two standard preconditioners: Jacobi and Incomplete Cholesky (ichol). This research was conducted from August to December 2021 in conjunction with Sandia National Laboratories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Randomized Cholesky Preconditioning for Graph Partitioning Applications

Graph partitioning has emerged as an area of interest due to its use in various applications in computational research. One way to partition a graph is to solve for the eigenvectors of the corresponding graph Laplacian matrix. This project focuses on the eigensolver LOBPCG and the evaluation of a new preconditioner: Randomized Cholesky Factorization (rchol). This proconditioner was tested for its speed and accuracy against other well-known preconditioners for the method. After experiments were run on several known test matrices, rchol appears to be a better preconditioner for structured matrices. This research was sponsored by National Nuclear Security Administration Minority Serving Institutions Internship Program (NNSA-MSIIP) and completed at host facility Sandia National Laboratories. As such, after discussion of the research project itself, this report contains a brief reflection on experience gained as a result of participating in the NNSA-MSIIP.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

PACT Module Preconditioning Protocol (V.0.1)

The purpose of this protocol is to bring metal halide perovskite (MHP) modules to a repeatable and relevant state prior to making a performance measurement. Performance measurements are made before and after a stressor has been applied to the module to quantify the degree of loss resulting from the stressor. This procedure is intended to be carried out both before and after the accelerated test.

14 SOLAR ENERGY↗